Figure 8

The \(d'\)-strength \(s_{d'}(v)\) versus the the d-strength \(s_{d}(v)\) of a node v when \((d',d)\) is equal to (3,2) (blue line), (4,2) (yellow line) and (4,3) (green line) respectively in each collaboration network. Each axis (e.g., \(s_{d}(v)\)) has been normalized by its maximum (e.g., \(max_{v}(s_{d}(v))\)). Only nodes whose d-strength and \(d'\)-strength are both non-zero are considered. The dashed line represent the reference case \(\frac{s_{d'}(v)}{max_{v}(s_{d'}(v))} = \frac{s_{d}(v)}{max_{v}(s_{d}(v))}\), where \(d'\)-strength is a linear function of the d-strength of nodes. Note that both axes are presented in logarithmic scales. In total 30 logarithmic bins are split for horizontal axis.